Methods, systems, and devices for designing and manufacturing flank millable components

ABSTRACT

Methods, systems, and devices for designing and manufacturing flank millable components. In one embodiment, devices, systems, and methods for designing a flank millable component are provided, in which a user is notified when a component geometry option is selected that will result in the component not being flank millable. In another embodiment, the user is prevented from selecting a geometry option that would result in the component not being flank millable. In yet another embodiment, devices, systems, and methods are provided for manufacturing a component with a flank milling process, in which optimized machine instructions are determined that minimize milling machine motion.

RELATED APPLICATION DATA

This application is a non-provisional of U.S. Provisional PatentApplication Ser. No. 61/982,609, filed Apr. 22, 2014, entitled “Methods,Devices, and Systems for Flank Milling a Turbo-Machinery Component,”which is incorporated by reference herein in its entirety.

FIELD OF THE INVENTION

The present invention generally relates to the field of design andmanufacture of turbomachinery components. In particular, the presentinvention is directed to the design of flank millable turbomachinerycomponents and methods of determining milling instructions for flankmilling turbomachinery components.

BACKGROUND

Turbomachinery components can be designed using computer automateddesign (CAD) software to generate a dataset representing the shape ofthe component. Computer automated manufacturing (CAM) software can thenbe used to translate the data set into a series of machininginstructions for manufacturing the component.

Turbomachinery components are often manufactured by a machining processwhereby material is removed from a work piece with a mill having arotary cutter. Significant advancements in machining time, parttolerances, and part finishes have been realized by employing a flankmilling process, where the side of an elongated cutter is used to removematerial, rather than the end of the cutter, which is utilized in apoint milling process. Flank milling, however, can only be used tomachine certain geometries and state of the art turbomachinerycomponents often have very complex shapes. In addition, modern CADsoftware provides designers with great flexibility for designingcomponents, enabling complex design processes to optimize componentgeometry. This high degree of flexibility can lead to the design of acomponent that will be difficult or impossible to flank mill. Thedesigner, however, may not realize he or she has designed a componentthat cannot be flank milled until very late in the design process, forexample, not until prototyping or manufacturing. At that point thedesigner is in an undesirable position choosing between proceeding witha less efficient and more costly manufacturing process such as pointmilling, or going back and re-designing the component. And even if aflank millable geometry is input into the CAM software, the machineinstructions calculated by the CAM program can result in excessivemachine motion and undesirably long machining times.

SUMMARY OF THE DISCLOSURE

In one implementation, the present disclosure is directed to a method ofdesigning a turbomachine blade having a flank millable edge. The methodincludes defining first and second blade surfaces extending between ahub section and a shroud section, each of the blade surfaces including aplurality of blade surface geometry quasi-orthogonal (QO) linesextending between the blade surface hub and shroud sections; defining arounded blade edge having a ruled surface and extending in a spanwisedirection across the blade between an edge portion of the hub sectionand an edge portion of the shroud section and extending in a flowwisedirection from a first edge transition line adjacent the first bladesurface to a second edge transition line adjacent the second bladesurface; and selecting an edge shape distribution that results in thefirst edge transition line being substantially aligned with one of thefirst blade surface QO lines and the second edge transition line beingsubstantially aligned with one of the second blade surface QO lines.

In another implementation, the present disclosure is directed to amachine-readable medium containing non-transitory machine-executableinstructions for a turbomachinery component computer automated design(CAD) program. The machine-readable medium includes a blade geometryprogram for specifying a blade geometry including a blade surfacedefined by geometry quasi-orthogonal (QO) lines extending between huband shroud sections; and an edge geometry program for specifying aflank-millable rounded edge, the edge geometry program includinginstructions for: receiving a user-specified edge shape selection; andgenerating an edge shape distribution having an edge transition that issubstantially aligned with one or more of the blade surface QO lines.

In yet another implementation, the present disclosure is directed to amethod of designing a turbomachine blade having a natural frequency. Themethod includes defining a blade surface having hub and shroud sectionsand a plurality of blade surface quasi-orthogonal (QO) lines extendingbetween the hub and shroud sections; defining a blade edge having aruled surface including a plurality of edge QO lines extending betweenthe hub and shroud sections; and defining a shape distribution of theblade edge including: applying a constraint on the blade edge shapedistribution requiring a first edge QO line to have a within-tolerancedifference in location and orientation from an adjacent blade surface QOline that will result in a flank-millable edge shape; and adjusting theblade edge shape distribution to adjust the natural frequency of theblade.

In still another implementation, the present disclosure is directed to aturbomachinery component that includes a plurality of blades each havinga pressure surface, a suction surface, and leading and trailing edges,wherein at least one of the leading and trailing edges has a roundedshape and was machined with a flank milling machining operation.

In still yet another implementation, the present disclosure is directedto a method of flank milling a turbomachinery component with a millingmachine having a work piece table and a rotary cutter. The methodincludes placing a work piece on the work piece table; receivingmachining instructions for flank milling the work piece, the machininginstructions including instructions for forming a turbomachinery bladehaving a blade surface and a rounded edge by performing a continuousflank milling motion along the blade surface and rounded edge; andmachining the work piece according to the machining instructions withthe rotary cutter.

BRIEF DESCRIPTION OF THE DRAWINGS

For the purpose of illustrating the invention, the drawings show aspectsof one or more embodiments of the invention. However, it should beunderstood that the present invention is not limited to the precisearrangements and instrumentalities shown in the drawings, wherein:

FIG. 1 is a flow diagram illustrating a method of designing a flankmillable component and manufacturing the component with a flank millingprocess;

FIG. 2 is a perspective view of an exemplary five-axis milling machine;

FIG. 3 is a top view of an exemplary turbomachinery component that canbe designed to be flank millable and then machined using optimizedmachining instructions;

FIG. 4 is a flow diagram illustrating a method of designing a flankmillable component;

FIG. 5 is an example graphical user interface for implementing a methodof designing a flank millable component;

FIG. 6 is an example graphical user interface for implementing a methodof designing a flank millable component;

FIG. 7 is a cross sectional view, in a meridional plane, of a FullyRadial turbomachinery blade geometry with geometry quasi-orthogonallines;

FIG. 8 is a cross sectional view, in a meridional plane, of a FullyRadial turbomachinery blade geometry with flow quasi-orthogonal lines;

FIG. 9 is an example graphical user interface for implementing a methodof designing a flank millable component;

FIG. 10 is a perspective view of a turbomachinery impeller having aplurality of blades with swept leading edges;

FIG. 11 is a perspective view of a turbomachinery blade having a shearededge;

FIG. 12 is a perspective view of a turbomachinery blade having a roundededge;

FIG. 13A is a perspective view of a turbomachinery blade having arounded leading edge;

FIG. 13B is a detailed view of the leading edge of the turbomachineryblade of FIG. 13A;

FIG. 14 shows cross-sectional geometrical proportions of theturbomachinery blade of FIGS. 13A and 13B at hub and shroud sections;

FIG. 15 shows cross-sectional geometrical proportions of anotherturbomachinery blade;

FIG. 16A is a perspective view of the turbomachinery blade of FIG. 15;

FIG. 16B is a detailed view of the leading edge of the turbomachineryblade of FIGS. 15 and 16A;

FIG. 17 shows an example blade geometry defined by geometry QO lines andapproximate flank milling cutter orientations required for flank millingthe blade;

FIG. 18 shows another example of a blade geometry defined by geometry QOlines and approximate flank milling cutter orientations required forflank milling the blade;

FIG. 19 is a flow diagram illustrating a method of designing a flankmillable component;

FIG. 20 is a flow diagram for a sub-routine of the method shown in FIG.19;

FIG. 21 is a flow diagram for a sub-routine of the method shown in FIG.19;

FIG. 22 is a flow diagram for a sub-routine of the method shown in FIG.19;

FIG. 23 is a flow diagram for a sub-routine of the method shown in FIG.19;

FIG. 24 is a flow diagram illustrating a method of calculating millingmachine instructions for flank milling a part;

FIG. 25 is a perspective view of an initial position of a millingmachine rotary cutter;

FIG. 26 is a perspective view of the cutter of FIG. 25, and also showingan amount of undercut;

FIG. 27 is a perspective view of the cutter of FIG. 25 in an alternativeorientation;

FIG. 28 is a flow diagram illustrating a method of calculating millingmachine instructions for flank milling a part;

FIG. 29 is a perspective view of a cutter and a turbomachinery bladesurface;

FIG. 30 is side views of exemplary types of milling machine cutters;

FIG. 31 is an illustration of cutter positions along a machine path;

FIG. 32 is an illustration of a subset of the cutter positions in FIG.31;

FIG. 33 is a flow diagram illustrating a method of designing a flankmillable component with improved manufacturability; and

FIG. 34 is a diagram illustrating a machine capable of implementingvarious aspects of the present disclosure.

DETAILED DESCRIPTION

Some aspects of the present invention include devices, methods, andsystems for designing a component that can be machined, at least inpart, with a flank milling machining process. Methods of designing aflank millable component include monitoring component geometry optionsselected by a designer and notifying the designer when a geometry optionis selected that will result in the component no longer being flankmillable. Other aspects include providing the designer with options tomodify the component geometry to make the component flank millable. Aswill be seen below, such feedback during the design process can beinvaluable, ensuring the final component design will be flank millableand avoiding the undesirable situation of not learning until too late inthe product design phase that a component cannot be flank milled. Otheraspects of the present invention include improved methods of calculatingflank milling machining instructions that determine an optimizedmachining path that results in reduced machining time and superiorsurface finishes without sacrificing accuracy of the shape of thecomponent. Yet other aspects of the invention include providing thecomponent designer with details on the manufacturability of thecomponent early in the design process.

FIG. 1 shows an example method 5 for designing and manufacturing a flankmillable component. As shown in FIG. 1, such a method can begin at step10, with the design of a flank millable component. As noted above, flankmilling involves using the side of a rotary cutter, rather than the endof the cutter, to remove material from a work piece. Designers andmanufacturers often try to design components with flank-millablegeometries because flank milling can result in improved surface finishand significantly decreased manufacturing time and costs. For example,in the turbomachinery field, the costs for manufacturing aturbomachinery component such as an impeller can be quite high for anumber of reasons, including material hardness and complex geometries.Significant reduction in manufacturing time and costs have been realizedby utilizing flank milling. In step 10, the component may be designedusing computer automated design (CAD) which can involve CAD softwareoperating on one or more computer systems, such as the exemplary systemsillustrated in FIG. 34 and described in more detail below. A designer orother operator of the CAD software may select from a myriad of geometryoptions and geometry modifications to determine the final geometry ofthe component. During step 10, the CAD software may include variousprocesses that, as will be described in more detail below, areconfigured to notify the designer when the designer chooses a geometryoption that will result in a final component geometry that will mostlikely not be flank millable. Armed with this valuable information, thedesigner can make an informed decision to either proceed and design acomponent that will not be flank millable, or make appropriateadjustments to stay on a flank millable design path. In someembodiments, a CAD program may also include functionality for modifyingcomponent geometry to make the component flank-millable and/or improvemanufacturability, and may also include functionality for optimizing thestructural design of the component while maintaining a flank millablegeometry and adhering to the aerodynamic design intent.

After a flank millable component has been designed, at step 12, millingmachine instructions are calculated for machining the component. Themilling instructions can be determined using computer automatedmanufacturing (CAM) software that, as with the CAD software, can beimplemented on one or more computer systems such as the systemsillustrated in FIG. 28. The CAM and CAD software may be eitherintegrated in a comprehensive software package or exist separately.During step 12, a data set developed during step 10 that describes theshape of the component can be converted into machining instructions,such as the paths a milling machine cutter will take over a work pieceto remove material to obtain the final component geometry. During step12, the CAM software can include various processes and algorithms that,as will be described below, may be configured to calculate smoothmachining paths that eliminate excessive machine motion and reducemachining time, without compromising component geometry. In oneexemplary embodiment, a CAM program may include algorithms fordescribing an orientation of a cutter in a three dimensional system,such as a spherical coordinate system, and for simultaneously minimizingcutter motion in multiple dimensions, such as both angular planes of aspherical coordinate system, to find an optimal machining path. In someembodiments, the CAM software may include a simulator that allows themanufacturer to assess machining performance, such as machining time,machine motion, and accuracy before machining the part. The manufacturermay alter the optimized machining instructions based on the results ofthe simulation. After the machining instructions are determined, at step14, the part is machined using flank milling for at least a portion ofthe machining process. In addition the present disclosure, one or moreaspects contained in U.S. Provisional Patent Application Ser. No.61/720,166, filed Oct. 30, 2012, entitled “System and Method of FlankMilling a Turbo-Machinery Blade Using Ruled Surfaces,” and U.S.Non-Provisional patent application Ser. No. 14/067,652, filed Oct. 30,2013, entitled “Methods, Systems, and Devices For Designing andManufacturing Flank Millable Components,” both of which are incorporatedby reference herein in their entireties, may be utilized forimplementing one or more aspects of the present disclosure.

FIG. 2 shows exemplary milling machine 20 that may be used with theprocesses described herein to flank mill component 22 (also referred toherein as work piece 22). In one embodiment, milling machine 20 is afive-axis milling machine having work piece table 24 that can move intwo Cartesian directions and one rotary direction and head 26 that canmove in one Cartesian direction and one rotary direction. Head 26 isconfigured to drive rotary cutter 28 which can be used to machine workpiece 22 mounted on work piece table 24. While the methods describedherein can be used to design and manufacture any number of differenttypes of components, work piece 22 shown in FIG. 2 and in greater detailin FIG. 3, is an exemplary turbomachinery component that can be designedto be flank millable using the processes disclosed herein and alsomachined using optimized machining instructions also disclosed herein.Component 22 is an exemplary impeller, having a plurality of blades 25(only three labelled to avoid clutter) that have ruled surfaces 29defined by guide curves 30 and 31 (only one of each labeled) connectedby geometry quasi-orthogonal (QO) lines 32 (also referred to herein asrulings 32). As used herein and described in more detail below, a ruledsurface can generally be assumed to be flank millable within typicaltolerances. A ruled surface is a surface that can be represented by twoor more guide curves, such as guide curves 30 and 31, connected by aplurality of geometry QO lines 32. Complex three dimensional surfacescan be ruled, and for some shapes, such as twisted surfaces, thestraight lines or rulings may not be parallel. In addition, somenon-ruled surfaces can also be flank milled. The methods of determiningimproved flank milling instructions described herein can also be used toflank mill some types of non-ruled surfaces.

FIG. 4 illustrates an exemplary process 40 for carrying out step 10 ofmethod 5 described above—designing a flank millable component. Process40 is an exemplary method that may be implemented in computer softwarecode, such as CAD software configured to design turbomachinerycomponents. Process 40 begins at step 42 with a user selecting a flankmillable option, which activates various processes described herein formonitoring the user's geometry selections. At step 44, the programmonitors the user's selections to determine if a selection has been madethat will result in a component that is not flank millable. If the userhas selected such an option, the process continues to step 46 andnotifies the user. After notifying the user, at step 48, if the user hasmade additional geometry selections, the program returns to step 44, andif not, at step 50 the process ends. In some embodiments, process 40also includes optional steps for providing the user with suggestions formodifying the component geometry to make it flank millable. Morespecifically, after notifying the user at step 46, the process at step52 may provide the user with suggestions for making the component flankmillable. At step 54, the exemplary program may determine whether theuser has accepted the suggestion, and if not, at step 50, the programends. In alternative embodiments, the program may provide a notificationthat process 40 will end because the user has declined to select a flankmillable geometry. In yet other embodiments, the process 40 candetermine whether the user has made a change other than the changesuggested at step 52 that results in a flank millable geometry, and ifso, continue to step 48 to determine whether the user has madeadditional changes. Returning to step 54, if the user accepts thesuggested change to the geometry, at step 56, the change is applied tomaintain a flank millable component design. The process then continuesto step 48 to determine if the user has made additional selections. Ifnot, at step 50 the process ends, and if so, the process returns to step44 to determine whether the additional selections will make the part nolonger flank millable.

FIGS. 5, 6, and 9 illustrate example graphical user interfaces (GUIs)that may be used to implement process 40. FIG. 5 illustrates an examplebasic geometry GUI 60 that provides basic component geometry options 62,64, and 66, as well as flank millable option 68 and sub-options tomaintain a flank millable geometry 70. As discussed above, a CAD programmay provide a user with a plurality of component geometry options, withsome options resulting in the component not being flank millable. Basicgeometry GUI 60 categorizes a plurality of basic geometry options aseither Type A geometries 62 that are normally flank millable, Type Bgeometries 64 that can be flank millable if additional sub-options areselected or modifications applied, and Type C geometries 66 that areassumed to be not flank millable. Flank millable option 68 is an exampleof an option monitored in step 42 of process 40 and, in the illustratedexample, selecting option 68 will activate the flank milling checks inprocess 40. Sub-options 70 can be one or more options that allow for atleast a portion of the component to be flank millable despite theselection of a geometry that could otherwise make the component nolonger flank millable. For example, if the user selects a Type Bgeometry in category 64, the user could be prompted to select anappropriate sub-option 70 to maintain the component as flank millable.In addition, as discussed in more detail below, the user may select amodification to one of the basic geometry models in categories A or Bthat would result in the component no longer being flank millable or atleast the program no longer considering the component as being flankmillable. In such a case, the user may be prompted to select anappropriate sub-option 70 to maintain a flank millable geometry, or torelax certain design constraints so the program can consider thegeometry as flank millable.

FIG. 6 illustrates an exemplary basic geometry GUI 74 having a pluralityof basic geometry options 76 for designing a turbomachinery component.GUI 74 also has a flank millable option 78 and sub-options 80. In theexemplary GUI 74, “Independent hub and shroud,” “Explicit shroud, radialinlet, exit rake,” “NACA 65 Airfoil blades,” “CETI (Patented),” “Specifyshroud and lean angle,” “Use blade sections defined in Z,” and “RTheta2D Wedge Diffuser” are basic turbomachinery blade geometry options thatcan be defined by ruled surfaces, or in other words, can result in aflank millable component and would be considered a Type A geometry 62 inexample GUI 60. “Fully radial,” “2-D with Bezier beta distribution,”“2-D with straight or circular arc blades,” and “Use a separate bladegenerating sheet” would be considered Type B geometries 64 requiringadditional checks to ensure the component is flank millable. 2D WedgeDiffuser,” “Custom,” and “Specify hub and extrusion direction” would beconsidered Type C geometries, or in other words, are assumed to be notflank millable. As will be appreciated by a person of ordinary skill inthe art (POSIA), any number of other blade geometry options whethercurrently existing or developed in the future, may be included andcategorized into types A-C geometries. In one exemplary embodiment, if auser has selected a Type C geometry, flank millable option 78 may begreyed out, or otherwise not selectable. In another embodiment, if theuser selects flank millable option 78 after selecting a Type C geometry,the program would warn or prompt the user that a flank millable geometryis not available for the basic geometry model selected.

The “Fully radial,” “2-D with Bezier beta distribution,” “2-D withstraight or circular arc blades,” and “Use a separate blade generatingsheet” geometries are exemplary Type B geometries because someadditional modification(s) or sub-option(s) must be made or selected toensure the resulting component geometry is flank millable. In thisexample, these geometries fall under Type B because they have the commoncharacteristic of being defined by a zero-thickness mean camber sheetwith a separate user-defined thickness from the mean camber sheet. Asdiscussed above, a surface defined by ruled elements can be assumed tobe flank millable. In one embodiment, if a user selects one of thesegeometries, the geometry will be considered flank millable if the userdefines the thickness of the blade along ruled lines. If the userdefines the thickness along another set of lines, the geometry may beconsidered not flank millable. FIGS. 7 and 8 further illustrate twoexemplary options for defining the blade thickness for the “FullyRadial” blade geometry. FIG. 7 illustrates a blade shape 82 defined byruled line elements, or geometry QO lines 84. As shown in FIG. 7, in theillustrated embodiment, geometry QO lines 84 have a constant Z and thetain a cylindrical coordinate system. By contrast, FIG. 8 illustrates thesame blade shape 82 defined by flow QO lines 86 that, as is known bypersons having ordinary skill in the art, are lines that arequasi-perpendicular to a working fluid flow direction and used tocalculate working fluid flow. If the user defined a thickness from themean camber sheet along the flow QO lines rather than geometry QO lines84, the resulting surface may not be defined by straight or ruled lines.Thus, additional checks are necessary for these example Type Bgeometries, here, checking the thickness definition, to confirm theblade will be flank millable. As will be appreciated, CAD programs madein accordance with the present disclosure may have similar checks ormodifications for other component geometries having other geometry andflow QO line orientations.

In the example embodiment, the “Fully radial,” “2-D with Bezier betadistribution,” and “2-D with straight or circular arc blades,” have thecommon characteristic that thickness is normally applied along flow OQlines, but if the thickness were applied along the geometry QO lines,the resulting change in component geometry is typically very small.Thus, in one embodiment, when a user selects one of these three Type Bgeometries, and has selected the flank millable option 78 (FIG. 6), theCAD program may automatically apply the user's thickness definitionalong geometry QO lines, rather than flow QO lines to ensure thecomponent will have a ruled surface. In an alternative embodiment, theprogram could warn the user that the thickness must be applied along thegeometry QO lines and ask if the thickness definition should be appliedalong the geometry QO lines. In yet another embodiment, the programcould perform an additional check to evaluate the effect of changing thethickness from flow to geometry QO lines on the shape of the componentand only change the thickness automatically if the difference is lessthan a predetermined value.

The “Use a separate blade generating sheet” option (FIG. 6) is anexample of a Type B geometry 64 (FIG. 5) because the lines along theblade generating sheet on which the thickness definition is applied isseparately defined. Thus, additional sub-options must be selected toensure the geometry will be flank millable. FIG. 9 illustrates a GUIwith examples of user-defined sub-options 90 for the “Use a separateblade generating sheet” option. In this example, two sub-options arerelevant to ensuring the geometry is flank millable. Sub-option “Lineartheta from hub to shroud” 92 should not be selected because it woulddefine a mean camber sheet that is not ruled in (x,y,z) space, andsub-option “Thickness based on the blade generating lines” 94 should beselected because it will apply thickness along the geometry QO lines.

Referring again to FIG. 6, basic geometry GUI 74 may have sub-options 80to maintain flank millable geometry that can be selected to provide auser with increased flexibility in blade geometry options while stillmaintaining a blade geometry that will be, at least in part, flankmillable. Exemplary sub-options 80 may include “Allow for point milledleading and trailing edges” 96 and “Allow more than two sections torepresent the blade shape” 98. Sub-options 96 and 98 are examples ofgeometry options that allow the program to consider more complex shapesflank millable so that a user can modify a basic geometry, such as oneof the basic geometry options 76, while still maintaining a surface thatthe program considers flank millable.

Sub-option “Allow more than two sections to represent the blade shape”98 may be used in situations where the user modifies an otherwise flankmillable blade geometry such that additional sections are needed tofully describe the blade. For example, FIG. 10 shows an exampleturbomachinery impeller 100 having a plurality of blades 101 with sweptleading edges 102. In this example, dotted line 103 represents theleading edge for the original basic blade geometry. The geometry ofblades 101 were modified with an edge cut, here an end portion of theblades being removed, resulting in swept leading edges 102. The originalbasic blade geometry could be represented by two sections—a hub guidecurve or section 104 and a shroud guide curve or section 105. Beforemaking the edge cuts, the program would consider blades 101 to be flankmillable because the blades could be represented by two sections ruledline elements 106 (also referred to as geometry QO lines 106) extendingbetween. The edge cuts for the swept leading edge 102, however, cutacross ruled line elements 106 such that the entire surface of blade 101can no longer be represented by line elements 106 extending between twosections 104 and 105. Sub-option 98, however, allows the user to relaxthe constraints the CAD program uses to determine whether blades 101 areflank millable. By selecting sub-option 98, the program will allow forthe addition of one or more guide curves to bound ruled line elements106 that no longer extend from curve 104 to curve 105. Thus, if a userselects the flank millable option 78 (FIG. 6) and adds a swept leadingor trailing edge to an otherwise flank millable geometry, such that theentire blade can no longer be represented as a ruled surface with twoguide curves, the program can check to see if the user has selectedsub-option “Allow more than two sections to represent the blade shape”98 and if the sub-option is not selected, warn the user that the edgecuts makes a two section representation impossible. In alternativeembodiments, the program could also suggest that sub-option 98 beselected to allow the program to maintain at least a portion of theblade as flank millable.

FIGS. 11 and 12, illustrate another example of a geometry modificationthat may require the selection of additional sub-options to allow theprogram to describe at least a portion of the blade with a ruledsurface. As shown in FIGS. 11 and 12, blade 107 (FIG. 11) has a shearedleading edge 108, while blade 109 (FIG. 12) has a rounded leading edge110. A rounded leading edge that is straight and that can be defined byruled line elements can be flank milled, but if the rounded leading edgeis not, for example, if a rounded edge is added to a swept leading ortrailing edge, then without further modifications, it may no longer bepossible to represent the rounded edge with a ruled surface. Sub-option96 “Allow for point milled leading and trailing edge” (FIG. 6) providesincreased flexibility so that a user can specify a non-ruled roundedleading or trailing edge. If the user specifies a non-ruled rounded edgeon an otherwise flank millable shape and has selected sub-option 96, theprogram will consider the component flank millable, allowing for therounded edges to be defined separately and point milled. In an exemplaryembodiment, if a user selects the flank millable option 78 (FIG. 6) andselects an otherwise flank millable basic geometry from the basicgeometry options 76, but then specifies a non-ruled rounded trailing orleading edge, the program can check to see if the user has selectedsub-option “Allow for point milled leading and trailing edge” 96 and ifthe sub-option is not selected, warn the user that the rounded edge willrequire point milling. In an alternative embodiment, the program couldalso suggest that sub-option 96 should be selected to allow the programto maintain at least a portion of the blade as flank millable. Asdescribed below, exemplary CAD programs may also include edge geometryoptions that may allow a user to modify the geometry of a rounded edgethat is being applied to a swept leading edge that may allow the entireblade to be flank milled.

FIGS. 13A and 13B illustrate another example of a blade geometry 111having a ruled blade surface 112 that can be flank milled but having arounded leading edge 113 that likely requires either a separate flankmilling operation or a point milling operation because of the shapedistribution of the edge. As shown in FIGS. 13A and 13B, exemplary edge113 may be defined as a ruled surface with QO lines 114 extendingbetween edge portion 115 of hub section 116 and edge portion 117 ofshroud section 118 and may include edge transition 119 where leadingedge 113 begins. Unless otherwise specified, the terms shroud sectionand tip section as used herein are synonymous and both refer to thesection defining the extreme of a blade opposite a hub section of ablade. Unless otherwise specified, a blade referred to as having ashroud section or tip section may refer to any type of turbomachineblade. As shown in FIGS. 13A and 13B, the shape of edge 113 results inedge transition 119 that is not aligned or coincident with adjacentblade surface QO line 120 and that is spaced from and at a differentorientation than the blade surface QO line. Depending on the size of thespacing between blade surface 112 and edge transition 119 and the extentof the difference in orientation, such a spacing can make it difficultto machine the entire blade with a flank milling operation. For example,one or more of edge QO lines 114 may need to be modified such that theyare no longer linear resulting in an edge that is no longer defined by aruled surface. Even if the edge can be flank milled, the discontinuitybetween blade surface 112 and edge 113 can result in poor surface finishand longer machining times.

FIG. 14 illustrates the cross-sectional shape of rounded leading edge113, and shows the profile of edge 113 at edge portion 115 of hubsection 116 and edge portion 117 of shroud section 118. In theillustrated example, leading edge 113 has an elliptical shape, and has aconstant ellipse ratio across the entire edge, where the ellipse ratiois defined as the ratio of ellipse major to minor axis lengths. In theillustrated example, the blade does not have a constant width from hubto tip and instead a width w1 of the blade at the hub is greater than awidth w2 of the blade at the tip. With a constant ellipse ratio edgeshape, the varying blade width results in a corresponding variation inellipse major axis length along the blade edge, resulting in theflowwise length of edge 113 varying between hub and shroud edge portions115 and 117 and the resulting orientation of blade transition 119. Toflank mill a blade in a way that preserves the intended geometric shape,the orientation of the milling tool must be substantially parallel tothe QO lines. In the illustrated example, with the application of aconstant ellipse ratio, and as the ratio is increased, machining theleading edge becomes increasingly difficult using a flank millingtechnique and at a certain point may not be possible. Thus, the geometryof rounded leading edge 113 will likely result in blade 111 requiring aseparate point milling operation to machine the leading edge, whereas ifthe geometry of leading edge 113 was modified so that the orientation ofedge QO lines 114 was in closer agreement with the orientation ofadjacent blade surface QO line 120, a continuous flank milling operationcould be used for machining the blade.

FIGS. 15 and 16A and 16B illustrate one exemplary modification to theleading edge of blade 111 so that the blade can be manufactured with acontinuous flank milling operation. As shown, blade 111 may be modifiedto include a ruled leading edge 121 that can be flank milled bymodifying the shape of the edge. As shown in FIGS. 16A and 16B, in theillustrated example, the shape of leading edge 121 may be adjusted sothat edge transition 122 (where blade surface 112 ends and leading edge121 begins) is substantially aligned, or in some cases, substantiallycoincident with adjacent blade surface QO line 120. In yet other cases,an edge shape may be selected that results in edge transition 122 beingsubstantially parallel with adjacent blade surface QO line 120. As willbe appreciated by a person having ordinary skill in the art, the degreeof alignment between a edge transition and blade surface QO line that isrequired to flank mill the blade surface and the edge in a continuousmachining operation can vary and can depend on a variety of factors,including desired surface finish, desired machining time, and thecomplexity of the blade shape. In one example, a minimum degree ofalignment is required for enabling a continuous flank milling procedure,and closer alignment may result in improve manufacturability such asimproved surface finish and reduced cutter motion.

Such a modification can have a variety of benefits including reducingmachining time and costs and improving the surface finish of the blade.As shown in FIG. 15, in the illustrated example, the shape profile forleading edge 121 was adjusted from the constant ellipse ratio of leadingedge 113 of FIGS. 13-14 to a substantially constant ellipse major axislength, resulting in the blade having a varying ellipse ratio. In theillustrated example, a shape of blade 111 at edge portion 123 of shroudsection 118 was held constant and a shape at edge portion 124 of hubsection 116 and portions therebetween were adjusted to obtain a ruledsurface with QO lines that are substantially aligned with adjacent bladesurface 112 adjacent QO line 120. In one example, the ellipse major axisat edge hub section 124 may be set to the same as the ellipse major axisat edge shroud section 123 and a linearly or non-linearly varying shapedistribution may be applied between the edge hub and shroud sections.Thus, in one embodiment, rather than specifying a constant ellipseratio, a user may specify, e.g., a variable ellipse ratio or constantellipse major axis length, or hub and tip section shapes with linear ornon-linear variation between, etc., to define a rounded leading edgethat is flank millable.

As will be appreciated, the foregoing is provided merely by way ofexample and similar edge geometry modifications may be employed to anyrounded edge. The term rounded edge as used herein broadly refers to anyedge with a rounded profile, e.g., a rounded profile defined by anymathematical curve, including circular, parabolic, Bezier, etc. In oneexample, a CAD program may include features for defining leading andtrailing edge geometries that may allow a user to specify an edgegeometry at a hub or shroud/tip section. Exemplary programs may alsoallow a user to specify a constant or varying edge shape profile alongthe length of the edge, including shape profiles that vary both linearlyand non-linearly along the length of the edge. In another embodiment, auser may specify certain constraints on an edge shape, such aselliptical or parabolic and hub or tip geometry, etc. and the CADprogram may be configured to automatically determine an edge shapeprofile distribution that results in a ruled edge. In one example, theprogram may determine an edge shape profile resulting in the edgetransition that has a within-tolerance orientation to an adjacent bladesurface QO line. For example, the program may calculate an edge shapethat results in an edge transition that has a within-tolerance spacingfrom an adjacent blade surface QO line along both the hub and shroudsections 116, 118. For example, the program may evaluate a rate ofchange in blade surface QO line spacing along hub section 116 at alocation adjacent an edge transition and then confirm the rate of changealong the hub section between the last blade surface QO line and theblade transition is within a certain tolerance value of the bladesurface QO line spacing rate of change. The program may perform asimilar check along shroud section 118. If the rate of change in spacingalong either hub or shroud section 116, 118 is not within tolerance, inone embodiment, the program may adjust the edge shape distribution untilthe rate of change is within tolerance, indicating the orientation ofthe edge transition is sufficiently aligned with adjacent blade surfaceQO line orientation. In another embodiment, the program may notify theuser the edge transition is out of tolerance and allow the user tomodify the edge geometry. In another example, the CAD program maycalculate an edge geometry that results in a blade transition that issubstantially coincident with an adjacent blade surface QO line. In yetanother example, a CAD program may evaluate one or more of anorientation and location of a blade edge transition line and determinewhether the orientation and location are within a predefined toleranceof an adjacent first blade surface QO line where the predefinedtolerance may be based on a difference in spacing between adjacent firstblade surface QO lines proximate the first blade transition line.

In yet another example, a CAD program may include a graphical userinterface (GUI) that includes a dynamic display of a blade geometry andmay allow a user to manually adjust an edge shape by, e.g., enteringedge geometry inputs, and the GUI may automatically modify the graphicaldisplay showing the resulting change to edge geometry and change to edgetransition orientation. Such edge modifications can enable thedevelopment of blade geometries including rounded leading or trailingedges that may be machined with a continuous flank milling procedurewhile resulting in negligible changes to the aerodynamic design of theblade. Such modifications may also improve the manufacturability of ablade. For example, a first rounded edge shape that is flank millablemay be modified to have geometry QO lines that are in closer alignmentwith blade surface geometry QO lines, which may result in a smootherflank milling cutter motion, resulting in improved surface finish andreduce machining time.

Referring again to FIG. 6, in one example, if a user has selected option78 (create a flank millable blade surface) but has not selected option96 (allow for point milled leading and trailing edges) and has selecteda non-ruled leading or trailing edge, in addition to generating awarning that the selection will result in a blade that is not flankmillable, the program may ask the user if he or she wishes to employ oneof the edge geometry subroutines described above for modifying the edgeto make the edge flank millable. In one example, even if the user hasselected point milling option 96, the program may still notify the userwhen he or she has selected an edge geometry that will likely requirepoint milling and query whether the user wishes to modify the edgegeometry to make the edge flank millable.

In addition to modifying edge QO lines to improve manufacturability,blade surface QO lines may be modified in a way that has a minimalimpact on the aerodynamic design of the blade while having anappreciable impact on machining As noted above, to flank mill a blade ina way that preserves the intended geometric shape, the orientation ofthe milling tool must be substantially parallel to the QO lines. Thus,an orientation of blade surface geometry QO lines can have a directimpact on cutter orientation, cutter head motion, and surface finish.FIGS. 17 and 18 illustrate first and second blade geometries 125 and 126having first and second blade surface QO lines 127 and 128. FIGS. 17 and18 also conceptually illustrate three orientations 129A-C of a millingtool at three flowwise locations along blade 125 with a cutter tooldirection of movement illustrated by arrows A and similarly shows threecutter orientations 130A-C along blade 126 with a cutter tool directionof movement illustrated by arrows A. FIGS. 17 and 18 illustrate how thedifferent orientation of blade surface QO lines 127 and 128 can impactcutter orientation. As shown, the orientation of blade surface QO lines128 of blade 126 will likely result in improved machining time andsurface finish as compared to blade 125 because, as can be seen from acomparison of FIGS. 17 and 18, the orientation of QO lines 128 willresult in a smoother cutter motion, with a rate of change of the cutteralong hub and shroud sections 131 and 132 being more similar for blade126 than for blade A. For example, a comparison of cutter orientation129B for blade A to orientation 130B for blade 126 shows that for bladeA, to transition from orientation 129B to orientation 129C will involvesubstantially more cutter motion along hub section 131 than shroudsection G. Such uneven motion can negatively impact machine motion andsurface finish. By contrast, cutter orientations 130A-C suggest a moreeven rate of motion along hub and shroud sections 131 and 132 for bladeB.

In one example, blade geometry QO line orientation may be manuallymanipulated by the user to define a set of QO lines that maintainaerodynamic intent while improving machining. In another example, a CADprogram may have a subroutine for adjusting blade surface and/or bladeedge QO line orientation to minimize uneven cutter motion. In oneembodiment, a CAD subroutine may determine a rate of change in QO linespacing along a hub and shroud section and may adjust the orientation ofone or more of the QO lines when a rate of change along one of the huband shroud sections is not within a predefined tolerance of a rate ofchange along the adjacent corresponding portion of the hub or shroudsection. In some embodiments, the QO line orientation subroutine mayalso check other blade geometry values such as camber angle, thickness,and exit lean angle, etc. and not change the QO line orientation ifdoing so would result in an out-of-tolerance change to one or more ofthe blade geometry values. In another embodiment, a CAD program may beconfigured to calculate an estimated flank milling cutter motion speedalong the hub and shroud sections based on a set of blade surface QOlines and in one embodiment, the program may also include instructionsfor a flank milling optimizer user interface (UI) for displaying theestimated cutter speed and for receiving a user selection for specifyingor modifying geometry QO line orientation to reduce cutter motion orotherwise adjust flank milling performance. In some embodiments, theflank milling UI may also be configured to generate a graphical displayof the blade geometry including graphical indicators at blade locationswhere a difference between the hub and shroud cutter motion speed isgreater than a tolerance value, indicating locations of excess or unevencuter motion, which can aid a user in selecting optimal QO lineorientations. Thus, a combination of managing blade surface QO lineorientation and proper selection of edge shape, such as proper selectionof edge hub and tip ellipse ratios, allows for a blade surface shapethat can be machined using a flank milling process with a continuousmotion of the mill and for improved surface finishes from reduced cuttermotion.

As described above and more fully below, the edge shape designtechniques disclosed herein may be used to generate machininginstructions for machining a blade, where the blade may include a flankmillable edge. In one embodiment, a turbomachinery component may bemanufactured with one or more of the techniques disclosed herein and thecomponent may include a plurality of blades each having a pressuresurface, a suction surface, and leading and trailing edges, where atleast one of the leading and trailing edges have a rounded shape thatwas machined with a flank milling machining operation, where the roundededge may have an elliptical shape with a varying ellipse ratio. In someembodiments, the pressure surface, suction surface, and at least one ofthe leading and trailing edges may be machined with a continuous flankmilling machining operation. As will be appreciated by a person havingordinary skill in the art, such a turbomachinery component can differfrom a turbomachinery component having substantially the sameconfiguration but made by a different machining procedure. For example,a component that is machined from a continuous milling procedure mayhave an improved surface finish relative to a component manufactured byanother process. In addition, a turbomachinery component may bemanufactured with a flank milling procedure using a milling machinehaving a work piece table and a rotary cutter. In one example, a workpiece may be placed on the milling machine work piece table, andmachining instructions may be received for flank milling the work piece,where the machining instructions may include instructions for forming aturbomachinery blade from the work piece by performing a continuousflank milling motion to form a blade surface and rounded edge. Further,in some embodiments, machine instructions may include a series ofsequential cutter positions for machining the blade, where the cutterpositions include a first cutter position adjacent an end of the bladesurface and a second cutter position in series sequence with the firstcutter position adjacent an edge transition where the rounded edgebegins. In some embodiments, the orientation of the cutter in the firstcutter position is substantially parallel to an orientation of thecutter in the second position.

As shown in FIGS. 14 and 15, the exemplary modification to the leadingedge shape distribution resulted in a change in the shape of the leadingedge at the hub (compare the shape of edge 113 at edge hub section 115to the shape of edge 121 at edge hub section 124). While such a changecan, as discussed above, have a significant impact on manufacturability,such a change may have a negligible impact on the aerodynamic design ofthe blade due, in part, to the lower working fluid velocities proximatethe hub. Such a change, however, may also have an appreciable impact onthe structural characteristics and vibrational performance of theturbomachinery component. For non-limiting example, the illustrated edgeprofile modification from edge 113 to edge 121 may result in an increasein blade stiffness, raising the fundamental eigenfrequencies, and alsoincreasing the cross sectional area at the blade edge, helping to reduceblade bending stress. In one embodiment, such a change to the leadingedge shape may result in approximately a 0.5% to 20% change in the firstblade bending mode natural frequency. In another embodiment, adjusting ablade edge shape using the techniques disclosed herein may result inapproximately a 5% to 10% change. In yet another embodiment, theorientation of one or more blade surface QO lines may also be modifiedto adjust the natural frequencies of the blade. Thus, modification ofthe edge shape may be utilized to both enable a flank millable geometryas well as adjust the vibrational design of the blade. In oneembodiment, one or more of a CAD and finite element analysis (FEA)program may be utilized to design a leading or trailing edge shapeprofile that is both flank millable and that provides a desired naturalfrequency. For example, an edge geometry program may be configured toapply a flank-millable constraint on the blade edge shape distribution,such as requiring an edge transition to be aligned with blade surface QOlines, and also provide a variety of options for specifying or adjustingthe blade edge shape distribution to adjust the natural frequency of theblade to a desired value. Such a program may provide a powerful designtool for optimizing the vibrational performance and manufacturability ofthe blade. In one example, a modeling strategy can be used to controlblade stress and tune eigenfrequencies by increasing a thickness taperratio of an elliptical edge and locally controlling blade lean anglethrough varying the QO line orientation. The effect of QO position onblade eigenfrequencies can be quantified by performing simulations witha Finite Element Analysis program.

The foregoing discussion of specific basic blade geometries and bladegeometry modifications are merely exemplary embodiments implementing thebroader concepts disclosed herein. In alternative embodiments, themethods and processes described herein may be applied to a myriad ofother turbomachinery component geometries, as well as components otherthan turbomachinery components.

FIG. 19 illustrates exemplary method 132 for designing a flank millablecomponent, where a computer program, such as a portion of a CAD program,monitors component geometry throughout a design process and notifies auser if the component design veers from a flank millable geometry. FIG.19 illustrates at a high level, method 132, which includes, inter alia,sub-routines 133. Example embodiments of subroutines 133 are describedin more detail in connection with FIGS. 21-23. Method 132 begins at step134 with the user selecting a component geometry model, and at step 136,checks to see if the user has selected a flank milling option, such asflank millable option 78 (FIG. 6) indicating the user wants to design aflank millable component. If the user has not selected the flankmillable option, at step 137, the process ends. If the user has, at step138 the program checks the geometry model chosen by the user, and atstep 140, checks any geometry modifications made by the user. Duringsubroutines 133, the program can provide applicable warnings ornotifications 142 related to ensuring the blade is flank millable. Atstep 144 the program can check if such warnings are generated and if so,at step 146 can display the warnings and can also display suggestedfixes. At step 148 the program can check if the user has adopted any ofthe suggested fixes and if so, at step 150 can apply the fixes and thenat step 137 the program ends. In alternative embodiments, after step150, the program can monitor the component design for additionalchanges, and if changes are made, re-perform steps 136-150.

FIGS. 14 and 16 illustrate an exemplary embodiment of the check geometrymodel subroutine 138 (FIG. 19). The illustrated example of sub-routine138 begins with check basic geometry model subroutine 160 which checkswhether the basic geometry model selected, for example, the basicgeometry models 76 in example GUI 74 (FIG. 6), is flank millable. Afterchecking the basic geometry model, at step 162, the program determineswhether a geometry defined by a zero thickness mean camber sheet with aseparate thickness definition was chosen. If such a geometry was chosen,at step 164, the thickness definition is analyzed to determine whether alinear thickness has been defined. If such a selection was not chosen,subroutine 138 ends and the process continues to step 140 (FIG. 19). Atstep 164, if the thickness definition is not linear, the resulting bladesurface will not be ruled, so at step 166, a warning is generatednotifying the user that the blade will not be flank millable because ofthe non-linear thickness definition. After checking whether thethickness is linear, at step 168, the program checks whether thethickness is applied along ruled elements, or geometry QO lines, asdescribed above. If the thickness is not defined along ruled elements,at step 170, a warning is generated notifying the user that the bladewill not be flank millable unless the thickness is applied along ruledelements. Subroutine 138 then ends and the process continues to step 140(FIG. 19). As described above in connection with the Fully radial and2-D geometries shown in FIG. 6, in alternative embodiments, depending onthe specific blade geometry option, at step 168 the program may, insteadof warning the user, automatically change the thickness in apost-processing step so the thickness is applied along ruled elements ifthe difference in the resulting blade geometry is, for example, lessthan a predetermined value. If such an automatic change is made, theprogram may notify the user at step 170 that the change was made. Forother geometries, such as the “separate blade generating sheet” option(FIG. 6), at step 168, the program may check whether appropriatesub-options, such as sub-options 90 (FIG. 9) are selected in order todetermine if the thickness is applied along ruled elements. If theappropriate sub-option is not selected, at step 170 the program can warnthe user that the sub-option must be selected to maintain a flankmillable geometry. At step 168, if the thickness is defined along ruledelements, subroutine 138 ends and the process continues to step 140(FIG. 19).

FIG. 22 illustrates an exemplary check basic geometry model subroutine160, which checks for the selection of particular geometry options todetermine if any options have been selected that would result in thecomponent not being flank millable. The specific geometry optionsdiscussed herein are merely for illustrative purposes, and subroutine160 may vary according to the component type being designed and theparticular geometry options available. In the illustrated embodiment,subroutine 160 checks at step 174 whether an unknown geometry model hasbeen selected and if so, at step 176 warns the user that the blade isassumed to be not flank millable because the geometry is not recognized.If an unknown geometry model is not selected, at step 178 sub-routine160 checks if the geometry has more than two user controlled sections,and if so, at step 180 warns the user that the program will assume theblade will not be flank millable. If there are not more than twouser-controlled sections, at step 182, sub-routine 160 checks if thegeometry is ruled in non-Cartesian coordinates and if so, at step 184warns the user that the blade surface will not be ruled in (x,y,z)space. If the model is ruled in Cartesian coordinates, at step 186,sub-routine 160 checks if the blade edges are aligned with the ruledelement direction. If they are so aligned, subroutine 160 ends and theprocess continues to step 162 (FIG. 20). If not, at step 188, subroutine160 checks if the appropriate sub-option allowing the blade to berepresented by more than two sections, for example sub-option 98 (FIG.6) is selected. If not, at step 190, the program warns the user that theblade edges make a two-section representation impossible. In analternative embodiment, the program could suggest that an appropriatesub-option, for example, sub-option 98 (FIG. 6), must be selected. Atstep 192, the program checks whether the user has specified that theedges not aligned with a ruled element direction are rounded, and ifnot, subroutine 160 ends and the process continues to step 162 (FIG.20). If rounded edges are specified, at step 194 the subroutine checkswhether the user has selected a sub-option allowing for point milling aleading or trailing edge, such as sub-option 96 (FIG. 6). If the pointmilling leading and/or trailing edges sub-option is not selected, atstep 196, the program warns the user that the edges will require pointmilling. In an alternative embodiment, the program may also suggest thesub-option be selected to allow the program to consider the blade asotherwise flank millable. If the sub-option is selected, subroutine 160ends and the process continues to step 162 (FIG. 20). As mentionedabove, FIGS. 14 and 16 illustrate an exemplary check geometry modelsubroutine 138 (FIG. 19), which illustrates how basic geometryselections for a particular set of geometries for a particular type ofcomponent (turbomachinery blade) would be performed. In alternativeembodiments, the check geometry model subroutine may vary depending onthe type of component being designed and the geometry options availablein the particular CAD program.

Returning to FIG. 19, check modifications to geometry model sub-routine140 may include a variety of different implementations depending, inpart, on the geometry modification options provided by the CAD program.One example of check modifications to geometry model sub-routine 140 isillustrated in FIGS. 21 and 22. As described above, the geometry orshape of a component may be modified in a way that additionalsub-options must be selected to maintain the component as, at leastpartially, flank millable, or to allow the program to consider morecomplex shapes as flank millable. As shown in FIG. 21, examplesub-routine 140 begins at step 200, determining whether a basic geometrymodel has been modified. If not, subroutine 140 ends and the processcontinues to step 142 (FIG. 19). If a basic geometry model has beenmodified, in subroutine 202, the program checks whether the componentcan be considered flank millable despite the modification, including ifone or more required sub-options are selected that, for example, relaxthe constraints the program uses to determine if the component is flankmillable. If, at step 204, it is determined the modification will resultin a component that is not considered flank millable, at step 206, theprogram generates a warning, subroutine 140 ends, and the processcontinues to step 142 (FIG. 19). If at step 204 it is determined thegeometry can still be considered flank millable if certain sub-optionsare selected, then at step 208, the program determines whether thosesub-options have been selected. If such sub-options have been selected,sub-routine 140 ends, and if not, at step 210 the subroutine generatesthe appropriate warning and then the subroutine ends and the processcontinues to step 142 (FIG. 19).

FIG. 23 illustrates an exemplary embodiment of “check if flank millableif sub-option(s) selected” subroutine 202 (FIG. 21) applied to aturbomachinery component CAD program. Sub-routine 202 begins at step220, checking if a blade bowing option has been selected. If so,sub-routine 202 assumes the blade surface is no longer ruled and at step224 warns the user that selecting the bowing option will result in acomponent that is not flank millable. Whether or not blade bowing isselected, subroutine 202 continues to step 226, to check whether a bladetwisting option has been selected. If so, sub-routine 202 assumes theblade surface is no longer ruled and at step 228 warns the user thatselecting the twisting option will result in a component that is notflank millable. Whether or not the blade twisting option was selected,subroutine 202 continues to step 230 to check whether a fillet optionhas been selected, which, for example, adds a fillet or curved surfaceto the region where a blade meets the hub of an impeller. If the filletoption is selected, sub-routine 202 assumes the blade surface is nolonger ruled and at step 232 warns the user that selecting the twistingoption will result in a component that is not flank millable. Whether ornot a fillet option was selected, subroutine 202 continues to step 234to check whether a blade surface smoothing option has been selected. Ifso, at step 236 the program checks whether smoothing has been applied tomake a rounded leading or trailing edge, and if so, at step 238determines whether the rounded edge has been cut from the blade or addedto the basic blade shape. If the rounded edge was cut from the blade, atstep 239, sub-routine 202 checks whether the blade edges are alignedwith the blade surface ruled element direction, and if not, assumes therounding results in a blade surface that is no longer ruled and at step240 warns the user that selecting the smoothing option will result in acomponent that is not flank millable. In one embodiment, the subroutinemay query if the user wishes to employ one or more of the edgesubroutines disclosed herein for modifying a rounded edge shape to makethe blade flank millable. After performing the smoothing and roundededge checks in steps 234-239, subroutine 202 continues to step 242 tocheck whether any edge cuts have been applied, such as the example edgecuts discussed above in connection with FIG. 12. If so, at step 244 theprogram checks whether the edge cut results in a swept edge or diametertrim that modifies a leading or trailing edge, and if so, at step 246the program determines whether a sub-option allowing for the blade to berepresented by more than two sections, such as, for example sub-option98 (FIG. 6) has been selected. If such a sub-option has not beenselected, at step 248, a warning is generated that the swept edge ordiameter trim makes a two section representation impossible. In analternative embodiment, the program could also suggest that a sub-optionbe selected to allow the blade to be represented by more than twosections. At step 244, if the program determines the edge cut results ina swept edge or diameter trim that modifies a leading or trailing edge,at step 246 the program checks whether the sub-option allowing more thantwo sections has been selected and if so, at step 250, the program alsochecks whether the modified leading or trailing edge is rounded. If so,at step 251 the program checks whether the edges are aligned with theruled element direction, and if not, at step 252 checks whether asub-option allowing for point milling, such as example sub-option 96(FIG. 6) has been selected. If not, at step 254, a warning is generatedthat the rounded edge cut will require point milling. In one embodiment,the subroutine may also query if the user wishes to employ one or moreof the edge subroutines disclosed herein for modifying a rounded edgeshape to make the blade flank millable. In alternative embodiments, theprogram could also suggest that a sub-option allowing for point millinga portion of the blade be selected to allow the program to consider theremainder of the blade as flank millable. After performing the edgerounding checks of steps 250 and 252, the subroutine ends and theprocess continues to step 204 (FIG. 21).

In the example sub-routine 202 shown in FIG. 23, for many potentialblade modification options, such as bowing, twisting, fillets, andsurface smoothing, the example sub-routine assumes the blade is notflank millable if the particular options are selected. In alternativeembodiments, the program could perform additional checks and provideadditional sub-options that would allow the blade to be, at least inpart, flank millable despite the modification. For example, if a filletis applied, instead of assuming the fillet results in a blade that isnot flank millable, the sub-routine could allow the fillet portion ofthe blade to be represented by separate sections and, for example, pointmilled. Similar additions could be made for other geometry options toallow for more complex surfaces to be represented separately andmaintain a portion of the blade as flank millable.

Returning to FIG. 1, after step 10, where a flank millable component isdesigned, at step 12, milling machine instructions are calculated formilling the part. FIG. 24 illustrates step 12 in further detail. Asshown in FIG. 24, step 12 involves a first step 260, where a data setrepresenting the shape of a flank millable component is received. Atstep 262, the data set is converted into a series of cutter positions,such as positions of cutter 28 of 5-axis milling machine 20 (FIG. 2).

Referring again to FIG. 2, as described above, component 22 is anexemplary impeller, having a plurality of blades 25 that have ruledsurfaces 29 defined by guide curves 30 and 31 connected by straightlines or rulings 32. FIG. 25 illustrates the initial position of cutter28 (also shown in FIG. 2) determined in step 262 (FIG. 24). The positionshown in FIG. 25 is the “pure” geometric solution for flank milling ofruled surfaces, where cutter 28 is located tangent to ruled surfaceguide curves 30, 31 at the junctions of the rulings 32. The tangencybetween cutter 28 and the ruled surface is shown by line 280 (FIG. 25),which is coincident with a ruling 32. As discussed below, thisorientation can be referred to as an isoparametric-tangency orientation.The isoparametric-tangency orientation, however, can result ininaccurate machining results when the surface of the component beingmachined is curved or twisted. As shown in FIG. 26, when machiningcertain non-planar surfaces, cutter 28 can remove too much material,resulting in an undercut 282 represented by the difference between thedesired surface at ruling 32 and the actual path of the cutter,represented by line 284. Undercut 282 can, however, be minimized byre-orienting the cutter from an isoparametric-tangency orientation to anon-isoparametric tangency orientation. An exemplary non-isoparametrictangency orientation is shown in FIG. 27, where bottom portion 286 ofcutter 28 is kept at the location where a ruling 32 intersects guidecurve 31, and top portion 288 of the cutter is moved along guide curve30 to contact point 28, such that the contact curve between the cutterand the resulting surface represented by line 284 most closely matchesruled surface 29 and undercut 282 (FIG. 26) is minimized. In alternativeembodiments, top portion 288 could remain fixed and bottom portion 286could be moved along guide curve 30, or both ends of cutter 28 could beadjusted. Also, a reference point other than the guide curves could beused for the adjustment.

Thus, an undercut-minimized cutter orientation can be calculated forevery point along a surface by finding a deviation from theisoparametric-tangency orientation at each location. Anundercut-minimized solution, however, is often not desirable because itcan result in unacceptable milling machine motion. For example, therotary motion of milling machine head 26 (FIG. 2) can be unsmooth, andthere can be wild swings in work piece table 24 rotary motion,approaching 180° from one instruction to the next, even when there isonly a slight change in cutter orientation. Thus, a more optimizedmachining instruction is needed that results in a within-toleranceundercut while also providing smooth milling machine motion. Such anoptimized set of instructions is determined at step 264 (FIG. 28).

FIG. 28 illustrates an exemplary process for calculating machineinstructions for flank milling a work piece that results in withintolerance undercut while also minimizing machine motion, resulting insmooth machine motion and reduced machining time. At step 289, a datasetrepresenting a machined surface is received and an initial cutterorientation is calculated. FIG. 29 illustrates an exemplary coordinatesystem that may be utilized to calculate an optimized machine path. Atstep 289 a two parameter data set S(u,v) representing a machined surface290 (FIG. 29) of a component, is received. As shown in FIG. 29, surface290 can be represented by isoparametric guide curves 292 and 294,defined as u-curves with a constant v value. The orientation of cutter28 can be defined by the (x,y,z) location of cutter tip center 294,which is offset from point (u,v) by the cutter tip radius, and cutterorientation vector 296 defined in (Φ,θ) spherical coordinates, with thecutter orientation vector being directly related to the rotational axesof milling machine 20. FIG. 29 illustrates cutter 28 in an isoparametrictangency orientation with the cutter orientation vector 296 aligned withan isoparametric ruling along a constant u curve, indicated by cuttercontact point 298 at (u,0). To determine the initial cutter orientationat step 289 (FIG. 28), the program calculating the machininginstructions also receives information on the size and shape of thecutter 28. FIG. 30 illustrates exemplary cutter shapes that may be usedwith a milling machine such as milling machine 20, with possible cuttershapes including cylindrical with a ball end 300, conical with a ballend 302, cylindrical with a flat end 304, and conical with a flat end306. The shape and radius of the cutter is used to calculate the offsetof cutter tip center 294 from point (u,v) (FIG. 29), and cutterorientation vector 296.

With an initial cutter orientation determined, at step 308, a subset ofpoints along surface 290 are selected as fixed points and anundercut-minimized cutter orientation is calculated at each of thosepoints. FIGS. 31 and 32 provide a conceptual illustration of this step,where lines 310 (FIG. 31) represent all of the machining positions forsurface 290 and lines 312 (FIG. 32) are a subset of fixed points,representing a subset of positions 310, where an undercut-minimizedcutter orientation is determined. As described above, anundercut-minimized orientation can be determined by altering the angleof the cutter 28 with respect to the surface 290 (FIG. 29). In theillustrated embodiment, the undercut-minimized orientation is determinedby maintaining cutter tip 294 at point (u,v), and varying the contactpoint of cutter 28 along isoparametric guide curve 294 from point 298 at(u,0) to a point (u+/−Δu, 0) 302 (FIG. 29). At step 314, an initialcutter orientation is calculated for the remaining points, or unfixedpoints by linearly interpolating from the fixed points 312undercut-minimized orientations. At step 316 a machine motion ratio ischecked for each of fixed points 312 to determine whether any of theundercut-minimized orientations will result in excessive machine motion.It has been determined, for example, that near-vertical cutterorientations can result in large machine motion. In an exampleembodiment, the machine motion ratio is defined by the followingequation:

$\begin{matrix}{{{Machine}\mspace{14mu}{Motion}\mspace{14mu}{Ratio}} = \frac{{distance}\mspace{14mu}{the}{\mspace{11mu}\;}{tool}\mspace{14mu}{tip}\mspace{14mu}{travels}{\mspace{11mu}\;}{relative}\mspace{14mu}{to}\mspace{14mu}{the}\mspace{14mu}{machine}}{{distance}\mspace{14mu}{the}\mspace{14mu}{tool}\mspace{14mu}{travel}\mspace{14mu}{relative}\mspace{14mu}{to}\mspace{14mu}{the}\mspace{14mu}{workplace}}} & {{Eq}.\mspace{11mu}(1)}\end{matrix}$

At step 318, if the machine motion ratio for any of the fixed pointundercut-minimized orientations is greater than a predetermined value,then that point is unfixed and assigned an initial linearly-interpolatedorientation at step 314. The predetermined value can be any number, andcan be a user defined parameter. In an example embodiment, thepredetermined value can be set to 2 such that if the machine motionratio for any fixed point is greater than 2, that point will be removedfrom the subset of fixed points.

At step 320, an optimized cutter orientation is determined for each ofthe unfixed points. U.S. Pat. No. 5,391,024 entitled “Method forMulti-Criteria Flank Milling of Ruled Surfaces,” which is incorporatedby reference herein in its entirety, describes earlier approaches todetermining a machining path that sought to calculate machininginstructions resulting in within-tolerance undercut while minimizingmachine motion. Approaches described in U.S. Pat. No. 5,391,024 includeseparately interpolating cutter orientation vector Φ values and θvalues, and then using a empirically based scoring system to select oneof the two solutions. While those earlier approaches resulted inimproved machining instructions relative to calculating anundercut-minimized machine path, they still resulted in unsmooth machinemotion for certain shapes. At step 320, an improved calculation isutilized that determines an optimized machining path by simultaneouslyminimizing machine motion in both the Φ and θ directions. In an exampleembodiment, the optimization calculation is defined by the followingobjective function:

$\begin{matrix}{{S = {{\Sigma_{i = 3}^{n}\left( {\Delta^{2}\varphi_{i}} \right)}^{2} + \left( {\Delta^{2}\theta_{i}} \right)^{2}}}{where}} & {{Eq}.\mspace{14mu}(2)} \\{{\Delta^{2}\varphi_{i}} = {{\Delta\varphi}_{i} - {\Delta\varphi}_{i - 1}}} & {{Eq}.\mspace{14mu}(3)} \\{{\Delta\varphi}_{i} = \frac{\varphi_{i} - \varphi_{i - 1}}{d_{i} - d_{i - 1}}} & {{Eq}.\mspace{14mu}(4)} \\{{\Delta^{2}\theta_{i}} = {{\Delta\theta}_{i} - {\Delta\theta}_{i - 1}}} & {{Eq}.\mspace{14mu}(5)} \\{{\Delta\theta}_{i} = \frac{\theta_{i} - \theta_{i - 1}}{d_{i} - d_{i - 1}}} & {{Eq}.\mspace{14mu}(6)} \\{{\varphi_{i}\left( {\Delta\; u_{i}} \right)} = {\varphi_{io} + {\frac{d\;\varphi_{i}}{d_{u}}\Delta\; u_{i}}}} & {{Eq}.\mspace{14mu}(7)} \\{{\theta_{i}\left( {\Delta\; u_{i}} \right)} = {\theta_{io} + {\frac{d\;\theta_{i}}{d_{u}}\Delta\; u_{i}}}} & {{Eq}.\mspace{14mu}(8)}\end{matrix}$

-   Δφ_(i)=first finite difference-   Δ²φ_(i)=second finite difference-   φ_(i)=machine axis value φ at point i-   θ_(i)=machine axis value e at point i-   d_(i)=distance along machining path at point i

As shown in equation (2), the objective function S is defined as the sumof the squares of the second finite differences of the phi and thetamachining axes with Δu_(i) as the independent variable. The objectivefunction is minimized using standard mathematical techniques to findvalues of Δu. This is done by expanding the terms of the objectivefunction, setting ∂S/∂Δu_(i)=0, and solving the resulting system of5-banded linear equations. New values of phi and theta are thencalculated. The optimizer is called iteratively due to the linearapproximation of φ_(i)(Δu_(i)) and θ_(i)(Δu_(i)), and stops when thechange in the value of the objective function between subsequentcalculations is less than a predetermined value. As shown in equations 5and 6, a backward differencing scheme is utilized in the presentembodiment. In alternative formulations, a central or forwarddifferencing scheme could also be utilized.

The result of the machine-motion minimized calculation at step 320,where an objective function, such as objective function S (Eq. 2) isminimized, is an optimized cutter path where machine motion in both theΦ and θ directions is simultaneously minimized. The optimized cutterpath is reflected in new cutter orientation Δu values (FIG. 29) for eachof the unfixed points. Because the objective function S (Eq. 2) does notconsider undercut, at step 322, the undercut is checked at each of theunfixed points. At step 324, if the undercut at any of the unfixedpoints is greater than a predetermined value, then those points areadded to the subset of fixed points (step 308) where anundercut-minimized orientation is assigned. The process is then repeatedfor the remaining unfixed points to determine machine-motion minimizedorientations. The predetermined value used at step 324 can be a userdefined parameter and can vary depending on the acceptable tolerancesfor the component being machined, with a lower predetermined value beingset for parts having tighter tolerances.

In some embodiments, at step 326, additional machine motion control canbe added to one or more locations. For example, for some surfaces, the Φand/or θ curves calculated by the minimized objective function can havea high rate of change in certain areas, such as endpoints of the cutterpath. For those cases, the first finite differences of Φ and θ can beadded to the objective function S in regions of high motion which willresult in a flatter optimized Δu graph in those regions. In addition, insome exemplary embodiments, a user may specify the Δu values for one ormore locations to manually set the orientation to either minimizemachine motion or undercut, or both. At step 328, an optimized set ofmachining instructions is generated.

FIG. 33 illustrates a design process for designing a flank millablecomponent with improved manufacturability. At step 330, a designerutilizing a CAD program may select a flank millable option, such as theflank millable options disclosed herein, to ensure the final componentdesign is flank millable. At step 332, an initial flank millablegeometry is determined. At step 334, the CAD program includesfunctionality to translate the geometry into optimized machineinstructions, using for example, the methods disclosed herein fordetermining machine instructions that result in within-toleranceundercut while minimizing machine motion. At step 336, the CAD programcan perform a machining simulation to assess the machinability of thecomponent and determine, for example, locations of the component thatwill be difficult to machine or result in excessive machining time. Atstep 338, armed with this information, the designer may alter thecomponent geometry and then re-perform steps 334 and 336 until anoptimized component geometry is determined.

It is to be noted that any one or more of the aspects and embodimentsdescribed herein may be conveniently implemented using one or moremachines (e.g., one or more computing devices that are utilized as auser computing device for an electronic document, one or more serverdevices, such as a document server) programmed according to theteachings of the present specification and appropriate software codingcan readily be prepared by skilled programmers based on the teachings ofthe present disclosure. Aspects and implementations discussed aboveemploying software and/or software modules may also include appropriatehardware for assisting in the implementation of the machine executableinstructions of the software and/or software module.

Such software may be a computer program product that employs amachine-readable storage medium. A machine-readable storage medium maybe any medium that is capable of storing and/or encoding a sequence ofinstructions for execution by a machine (e.g., a computing device) andthat causes the machine to perform any one of the methodologies and/orembodiments described herein. Examples of a machine-readable storagemedium include, but are not limited to, a magnetic disk (e.g., aconventional floppy disk, a hard drive disk), an optical disk (e.g., acompact disk “CD”, such as a readable, writeable, and/or re-writable CD;a digital video disk “DVD”, such as a readable, writeable, and/orrewritable DVD), a magneto-optical disk, a read-only memory “ROM”device, a random access memory “RAM” device, a magnetic card, an opticalcard, a solid-state memory device (e.g., a flash memory), an EPROM, anEEPROM, and any combinations thereof. A machine-readable medium, as usedherein, is intended to include a single medium as well as a collectionof physically separate media, such as, for example, a collection ofcompact disks or one or more hard disk drives in combination with acomputer memory. As used herein, a machine-readable storage medium doesnot include a signal.

Such software may also include information (e.g., data) carried as adata signal on a data carrier, such as a carrier wave. For example,machine-executable information may be included as a data-carrying signalembodied in a data carrier in which the signal encodes a sequence ofinstruction, or portion thereof, for execution by a machine (e.g., acomputing device) and any related information (e.g., data structures anddata) that causes the machine to perform any one of the methodologiesand/or embodiments described herein.

Examples of a computing device include, but are not limited to, anelectronic book reading device, a computer workstation, a terminalcomputer, a server computer, a handheld device (e.g., a tablet computer,a personal digital assistant “PDA”, a mobile telephone, a smartphone,etc.), a web appliance, a network router, a network switch, a networkbridge, any machine capable of executing a sequence of instructions thatspecify an action to be taken by that machine, and any combinationsthereof. In one example, a computing device may include and/or beincluded in a kiosk.

FIG. 34 shows a diagrammatic representation of one embodiment of acomputing device in the exemplary form of a computer system 400 withinwhich a set of instructions for performing the methods disclosed herein.It is also contemplated that multiple computing devices may be utilizedto implement a specially configured set of instructions for causing thedevice to perform any one or more of the aspects and/or methodologies ofthe present disclosure. Computer system 400 includes a processor 404 anda memory 408 that communicate with each other, and with othercomponents, via a bus 412. Bus 412 may include any of several types ofbus structures including, but not limited to, a memory bus, a memorycontroller, a peripheral bus, a local bus, and any combinations thereof,using any of a variety of bus architectures.

Memory 408 may include various components (e.g., machine readable media)including, but not limited to, a random access memory component (e.g, astatic RAM “SRAM”, a dynamic RAM “DRAM”, etc.), a read only component,and any combinations thereof. In one example, a basic input/outputsystem 416 (BIOS), including basic routines that help to transferinformation between elements within computer system 400, such as duringstart-up, may be stored in memory 408. Memory 408 may also include(e.g., stored on one or more machine-readable media) instructions (e.g.,software) 420 embodying any one or more of the aspects and/ormethodologies of the present disclosure. In another example, memory 408may further include any number of program modules including, but notlimited to, an operating system, one or more application programs, otherprogram modules, program data, and any combinations thereof.

Computer system 400 may also include a storage device 424. Examples of astorage device (e.g., storage device 424) include, but are not limitedto, a hard disk drive for reading from and/or writing to a hard disk, amagnetic disk drive for reading from and/or writing to a removablemagnetic disk, an optical disk drive for reading from and/or writing toan optical medium (e.g., a CD, a DVD, etc.), a solid-state memorydevice, and any combinations thereof. Storage device 424 may beconnected to bus 412 by an appropriate interface (not shown). Exampleinterfaces include, but are not limited to, SCSI, advanced technologyattachment (ATA), serial ATA, universal serial bus (USB), IEEE 1294(FIREWIRE), and any combinations thereof. In one example, storage device424 (or one or more components thereof) may be removably interfaced withcomputer system 400 (e.g., via an external port connector (not shown)).Particularly, storage device 424 and an associated machine-readablemedium 428 may provide nonvolatile and/or volatile storage ofmachine-readable instructions, data structures, program modules, and/orother data for computer system 400. In one example, software 420 mayreside, completely or partially, within machine-readable medium 428. Inanother example, software 420 may reside, completely or partially,within processor 404.

Computer system 400 may also include an input device 432. In oneexample, a user of computer system 400 may enter commands and/or otherinformation into computer system 400 via input device 432. Examples ofan input device 432 include, but are not limited to, an alpha-numericinput device (e.g., a keyboard), a pointing device, a joystick, agamepad, an audio input device (e.g., a microphone, a voice responsesystem, etc.), a cursor control device (e.g., a mouse), a touchpad, anoptical scanner, a video capture device (e.g., a still camera, a videocamera), touchscreen, and any combinations thereof. Input device 432 maybe interfaced to bus 412 via any of a variety of interfaces (not shown)including, but not limited to, a serial interface, a parallel interface,a game port, a USB interface, a FIREWIRE interface, a direct interfaceto bus 412, and any combinations thereof. Input device 432 may include atouch screen interface that may be a part of or separate from display436, discussed further below. Input device 432 may be utilized as a userselection device for selecting one or more graphical representations ina graphical interface as described above.

A user may also input commands and/or other information to computersystem 400 via storage device 424 (e.g., a removable disk drive, a flashdrive, etc.) and/or network interface device 440. A network interfacedevice, such as network interface device 440 may be utilized forconnecting computer system 400 to one or more of a variety of networks,such as network 444, and one or more remote devices 448 connectedthereto. Examples of a network interface device include, but are notlimited to, a network interface card (e.g., a mobile network interfacecard, a LAN card), a modem, and any combination thereof. Examples of anetwork include, but are not limited to, a wide area network (e.g., theInternet, an enterprise network), a local area network (e.g., a networkassociated with an office, a building, a campus or other relativelysmall geographic space), a telephone network, a data network associatedwith a telephone/voice provider (e.g., a mobile communications providerdata and/or voice network), a direct connection between two computingdevices, and any combinations thereof. A network, such as network 444,may employ a wired and/or a wireless mode of communication. In general,any network topology may be used. Information (e.g., data, software 420,etc.) may be communicated to and/or from computer system 400 via networkinterface device 440.

Computer system 400 may further include a video display adapter 452 forcommunicating a displayable image to a display device, such as displaydevice 436. Examples of a display device include, but are not limitedto, a liquid crystal display (LCD), a cathode ray tube (CRT), a plasmadisplay, a light emitting diode (LED) display, and any combinationsthereof. Display adapter 452 and display device 436 may be utilized incombination with processor 404 to provide a graphical representation. Inaddition to a display device, a computer system 400 may include one ormore other peripheral output devices including, but not limited to, anaudio speaker, a printer, and any combinations thereof. Such peripheraloutput devices may be connected to bus 412 via a peripheral interface456. Examples of a peripheral interface include, but are not limited to,a serial port, a USB connection, a FIREWIRE connection, a parallelconnection, and any combinations thereof.

Exemplary embodiments have been disclosed above and illustrated in theaccompanying drawings. It will be understood by those skilled in the artthat various changes, omissions and additions may be made to that whichis specifically disclosed herein without departing from the spirit andscope of the present invention.

What is claimed is:
 1. A method of designing a turbomachine blade havinga flank millable edge, comprising: defining, with a processor, first andsecond blade surfaces of a computational model of a turbomachine blade,the first and second blade surfaces extending in a spanwise directionbetween a hub section and a shroud section, each of the blade surfacesincluding a plurality of blade surface geometry quasi-orthogonal (QO)lines extending between the blade surface hub and shroud sections;selecting, with the processor, a rounded blade edge shape for thecomputational model, the rounded blade edge shape having a ruled surfaceand extending in a spanwise direction across the blade between an edgeportion of the hub section and an edgesortion of the shroud section andextending in a flowwise direction from a first edge transition lineadjacent the first blade surface to a second edge transition lineadjacent the second blade surface, the rounded edge having a spanwiseshape distribution; and adjusting, with the processor, the spanwiseshape distribution so that the first and second blade surfaces androunded blade edge can be machined with a continuous flank millingoperation, the adjusting including adjusting the first edge transitionline to be substantially aligned with one of the first blade surface QOlines and adjusting the second edge transition line to be substantiallyaligned with one of the second blade surface QO lines.
 2. A methodaccording to claim 1, wherein said adjusting includes adjusting thespanwise edge shape distribution so that the first edge transition lineis substantially coincident with a first blade surface QO line adjacentthe edge.
 3. A method according to claim 1, wherein said adjustingincludes adjusting the spanwise edge shape distribution so that thefirst edge transition line is substantially parallel to a first bladesurface QO line.
 4. A method according to claim 1, wherein saidadjusting includes adjusting the spanwise edge shape distribution sothat the first edge transition line has an orientation and location thatis within a predefined tolerance of an adjacent first blade surface QOline.
 5. A method according to claim 4, wherein the predefined toleranceis based on a difference in spacing between adjacent first blade surfaceQO lines proximate the first blade transition line.
 6. A methodaccording to claim 1, wherein said selecting includes selecting anelliptical curved blade edge having major and minor axes and an ellipseratio equal to a ratio of the major and minor axes, and wherein saidadjusting includes adjusting the ellipse ratio to vary along theelliptical curved blade edge between the hub and shroud sections.
 7. Amethod according to claim 6, wherein said adjusting includes specifyingthe ellipse ratio at the edge portion of one of the hub or shroudsections and calculating a spanwise ellipse ratio distribution acrossthe blade.
 8. A method according to claim 1, wherein said adjustingincludes specifying an edge shape at one of the hub or shroud sectionsand calculating a spanwise shape distribution.
 9. A method according toclaim 1, wherein said adjusting further includes adjusting the spanwiseedge shape distribution to modify a natural frequency of the blade. 10.A method according to claim 9, wherein said adjusting includesspecifying an edge shape at one of the hub and shroud sections andvarying a flowwise length of the edge at the other one of the hub orshroud section to modify the natural frequency of the blade.
 11. Amethod according to claim 1, wherein said defining first and secondblade surfaces further includes: identifying one or more blade surfaceQO lines having an orientation that will cause increased or unsmoothmotion of a flank milling cutter and machine tool; and adjusting anorientation of the one or more of the blade surface QO lines to reduceor smooth the motion of the flank milling cutter and machine tool.
 12. Amethod according to claim 11, wherein said adjusting an orientation ofone or more of the blade surface QO lines includes selecting bladesurface QO line orientations that result in an estimated flank millingcutter speed along the hub section that is approximately the same as anestimated flank milling cutter speed along the shroud section.
 13. Anon-transitory machine-readable medium containing machine-executableinstructions for a turbomachinery component computer automated design(CAD) program comprising: a blade geometry program for specifying ablade geometry of a computational model of a turbomachinery component,the blade geometry program including instructions for specifying a bladesurface defined by geometry quasi-orthogonal (QO) lines extendingbetween hub and shroud sections; and an edge geometry program forspecifying a flank-millable rounded edge that can be machined with theblade surface in a continuous flank milling operation, the edge geometryprogram including instructions for: receiving, with a processor, auser-specified edge shape selection for the computational model of aturbomachinery component; and generating, with the processor, a spanwiseedge shape distribution for the user-specified edge shape selection thatresults in an edge transition being substantially aligned with one ormore of the blade surface QO lines.
 14. A machine-readable mediumaccording to claim 13, wherein the user-specified edge shape selectionis selected from the group consisting of edge ellipse ratio and edgeellipse major axis length.
 15. A machine-readable medium according toclaim 13, wherein the user-specified edge shape selection includes anedge ellipse major axis length at at least one of the hub and shroudsections and said generating includes calculating a spanwise edge shapedistribution having a varying ellipse ratio.
 16. A machine-readablemedium according to claim 13, wherein said edge geometry programincludes instructions for automatically calculating a flank millableedge shape distribution.
 17. A machine-readable medium according toclaim 13, further comprising a flank milling optimizer configured toestimate a flank milling cutter motion speed along the hub and shroudsections.
 18. A machine-readable medium according to claim 17, whereinthe flank milling optimizer further includes instructions for a userinterface (UI) for: receiving a user selection for specifying a geometryQO line orientation; calculating an estimated cutter motion speed basedon the user-selected geometry QO line orientation; and displaying theestimated cutter motion speed.
 19. A machine-readable medium accordingto claim 18, wherein the flank milling optimizer UI is furtherconfigured to generate a graphical display of the blade geometryincluding graphical indicators at blade locations where a differencebetween the hub and shroud cutter motion speed is greater than atolerance value.
 20. A method of designing a turbomachine blade having anatural frequency comprising: defining, with a processor, a bladesurface of a computational model of a turbomachine blade, the bladesurface having hub and shroud sections and a plurality of blade surfacequasi-orthogonal (QO) lines extending between the hub and shroudsections; defining, with the processor, a blade edge for thecomputational model, the blade edge having a ruled surface including aplurality of edge QO lines extending between the hub and shroudsections; and defining, with the processor, a shape distribution of theblade edge including: applying a constraint on the blade edge shapedistribution requiring a first edge QO line to have a within-tolerancedifference in location and orientation from an adjacent blade surface QOline that will result in a flank-millable edge shape; and adjusting theblade edge shape distribution to adjust the natural frequency of theblade.
 21. A method according to claim 20, wherein the edge QO linelocation and orientation tolerance is based on a difference in locationand orientation between adjacent blade surface QO lines proximate theblade edge.
 22. A method according to claim 20, wherein said adjustingincludes adjusting a shape of the blade edge proximate the hub section.23. A method according to claim 1, wherein the selecting includesselecting a rounded blade edge shape defined by a plurality of edgesurface geometry QO lines, further wherein the edge surface and bladesurface geometry QO lines are straight lines in three-dimensional space.24. A method of designing a turbomachine blade having a flank millableedge, comprising: defining, with a processor, first and second bladesurfaces of a computational model of a turbomachine blade, the first andsecond blade surfaces extending in a spanwise direction between a hubsection and a shroud section and each extending in a flowwise directionbetween a corresponding respective first and a second end, each of theblade surfaces having a flank-millable geometry; selecting, with theprocessor, a flank-millable rounded edge shape for the computationalmodel, the rounded blade edge shape extending in a spanwise directionfrom an edge portion of the hub section to an edge portion of the shroudsection and extending in a flowwise direction from a first edgetransition line adjacent one of the first blade surface ends to a secondedge transition line adjacent one of the second blade surface ends, therounded edge having a spanwise shape distribution; and adjusting, withthe processor, the spanwise shape distribution so that the first andsecond blade surfaces and rounded blade edge can be machined with acontinuous flank milling operation, the adjusting including adjustingthe first edge transition line to be substantially aligned with theadjacent first blade surface end and adjusting the second edgetransition line to be substantially aligned with the second bladesurface end.
 25. A method according to claim 24, wherein the first andsecond blade surfaces and the rounded edge are ruled surfaces.
 26. Amethod according to claim 24, wherein the selecting step includesspecifying an edge shape at a first spanwise location and the adjustingstep includes calculating the spanwise shape distribution that includesthe specified edge shape and that results in the first edge transitionline being substantially aligned with the adjacent first blade surfaceend and the second edge transition line being substantially aligned withthe adjacent second blade surface end.
 27. A method according to claim26, wherein the adjusting step includes varying a length-to-width ratioof the edge shape in a spanwise direction along the edge.